Peak level of play (Federer, Nadal, Djokovic & Co.)

Perhaps i dont understand AMs well enough, but isnt the AM of a player dependent on the opponent i.e. it is relative only to the opponent to the other side.

I suppose what one can deduce is whether players are performing "well" as compared to how they usually play. The AM can be used as a benchmark in matchups and whether they had a good day relatively speaking to past matches.

But to compare djokovic to federer for example..there is a small difference in AM. Is this because federer's opponents were better? They certainly performed "better" based on AMs, but this is relative to federer of course. As they can only play federer's shots not djokovic's.

Perhaps what we need is a Delta AM - that is the differene between the player and the opponent. That way we can potentially cancel out stylistic differences that would lead aggressive players to have a higher absolute AM than defense oriented players...

This way we have a better feel for the form of the player as compared to the competition.

Ferrer's form was clearly not that great, and he got smashed as predicted by the AMs. His opponents also subjectively were not necessarily tougher than novak's opponents, and they also performed worse that he did as per opponent's AM.

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Yes the AM would be dependent to some degree on the opponent. I think that must be true for almost any measurement in tennis; there are very few things that come to mind that don't depend to some degree on your opponent. Aces and double-faults come to mind; but once the ball reaches your opponent's racquet, you will have his shot to deal with (or his error to benefit from), and it's no longer completely in your hands, so to speak.

It's like counting winners and errors (the most common stats): you can definitely hit more winners if you're facing someone clearly inferior to you; it will not be much of a challenge for you to hit winners past him and to keep from making errors yourself.

That's why I like to use the AM's as a benchmark, like you say, in rivalries. If you keep the same two players constant the comparison is less problematic -- and that's especially true if you keep the surface constant, since surface speed has a great effect on AM's.

It becomes more complex if you're comparing the AM's that two players produce, not against each other, but against the field.

If you're asking why Djokovic and Federer produced similar AM's at this Australian Open, then it's definitely a question to ask, whether Federer's opponents were different in some way -- perhaps inherently superior, or inferior -- to Djokovic's opponents. If there's some large difference in the quality of opposition that Fed and Djok faced at this tournament, that would have an impact on the AM's that they produced.

However it's another thing simply to list as many AM's as you can for the top players in their entire careers. They all play the same competition on the same tour, so you would expect that their AM's can be compared fairly.

At that point, though, there are other issues, like style of play. Does style of play have an impact on AM's? Do AM's favor a certain style?

The more I think about that question the more complex the issue seems to be. We've all been working here on the assumption that SV reduces unforced errors and produces high AM's, because if two players are constantly rushing to net against each other, the defender will always be hitting passing shots or making forced errors, not UE's. And it's true that you can find many matches at Wimbledon, in older eras, where two SV players faced each other, coming in behind every serve, and making very few UE's. Hence they have high AM's.

But there's a twist here: at the most basic level, you get a high AM by keeping your unforced errors down. There's a real opportunity in that sense for players like Borg or Nadal, who are masters at keeping their UE's down, to post high AM's. You can force these men into errors, but they will rarely hand you a point for free. And with low UE's, their AM's have to be high.

By the same token, an aggressive net-rushing player facing a great defender will have no choice but to make a lot of UE's: because they have to go for their shots if they're going to win; and in going for their shots they will make plenty of UE's.

So it's not true that merely having an aggressive style will get you high AM's, while the grinders will have low AM's. That really depends on the matchups.

It's true that two net-rushers facing each other tend to crowd out opportunities to make UE's and they will often post extremely high AM's; and two grinders facing each other will have nothing but opportunities to make unforced errors, so in such matches you will often see low AM's.

But an aggressive player facing a grinder is a different story. I don't know that there is any inherent advantage there, as far as AM's go. The aggressor might easily make a ton of UE's errors, and post a low AM; while the defender might easily get a high AM by making almost no errors.

Upthread we had a discussion about Nadal, because he seems to be the archetype of the grinder who hits a low number of winners and makes a low number of errors. I thought that if we looked at his winner/error differentials, we might find low numbers. But I have found the opposite to be true: when he wins his matches Nadal has a better winner/error differential than his opponents even when he's playing a mega-aggressive player. Nadal might make far fewer winners than someone like Verdasco; but he also makes far fewer errors; and if Nadal wins the match he will almost always have a higher winner/error differential than Verdasco. Just because Nadal's numbers of winners and errors are low, does not mean that he ends up with low winner/error differentials: or to put it another way, just because his winners and errors are low does not mean that he can't post a higher Aggressive Margin. An Aggressive Margin is just the margin of your forcing plays as compared to your errors. Your winners and errors might be low but all you have to do is keep your winners ahead of your errors better than the other guy does, and you win the match.

The absolute figures don't matter here. Nadal can post 50 winners while Verdasco posts 100. The only important question is, if Nadal posts 50 winners while making 30 errors (+20), can Verdasco post his 100 winners while making no more than 80 errors? Can Verdasco, in short, keep ahead of his own errors by a margin of +20? If he can't, he will probably lose that match to Nadal. If Verdasco can only keep ahead of his own errors by 10, while Nadal is keeping ahead by 20, then Nadal will come out at the end having won more points: and that almost always means that Nadal will win the match.

The higher Aggressive Margin, mathematically, always goes to the player who wins the most points.

So why should there be an advantage there for either an aggressive style or a defender's style? All you have to do is keep ahead of your own errors better than the other guys does.

If anything -- I'm not pushing this, but if anything -- someone with heavy topspin who is ridiculously good at keeping his errors down will naturally be posting high AM's.

That's why, against expectation, Nadal posted AM's above 40% even at the 2006 Wimbledon. I mean, it's true that Nadal is caricatured as being nothing but a dirtballer with a forehand in his early days; in fact he could do a lot more; but even so, he's the classic archetype of a defender; and even in '06, before the more "aggressive" facets of his game (like his serve, or his volley) had matured, he was posting these ridiculously high AM's. On grass.

How does something like that happen, if in fact the AM method favors aggressive players who are all about hitting winners?

It's a complex issue, and the style question is a valid one, when it comes to AM's. But it's not straightforward at all.

As far as Nadal goes, I think those numbers from the '06 Wimbledon already show that he was better on grass than he is often given credit for. But we would have to regard him as even an even better grasscourter than that, in '06, if we decided that the AM method really does make aggressive players look better: because then Nadal is posting these high AM's despite the method being inherently biased against him.

I don't think we need to go that far, because I don't think it's been shown that the AM method is inherently advantageous to aggressive players.

so fed-tsonga was better match quality wise when compared to djoker-stan going by the AMs .....not by a small margin ... question is how much better was it and how much of the difference was caused by djoker's insane defense ?

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Some of the issues here I addressed in the last post above. Just would add a few things.

Djoker's defense was insane but he was not necessarily playing to his best level -- which is arguably one reason for Wawrinka getting so close to beating him. The commentators were saying late in the match that he had been missing a good number of FH's when he went for winners. I think they said that when he had a sitter than he dumped into the net, going for a DTL winner. That was on break point; if Novak had converted he would have been serving at 5-3, for the match. It all could have ended a lot sooner.

Now on the other hand, his defense was ridiculous. I'm just saying there could be another side to that: he found himself in a greater number of long rallies, and in such a long match, because at times his offense was failing him.

Some of the issues here I addressed in the last post above. Just would add a few things.

Djoker's defense was insane but he was not necessarily playing to his best level -- which is arguably one reason for Wawrinka getting so close to beating him. The commentators were saying late in the match that he had been missing a good number of FH's when he went for winners. I think they said that when he had a sitter than he dumped into the net, going for a DTL winner. That was on break point; if Novak had converted he would have been serving at 5-3, for the match. It all could have ended a lot sooner.

Now on the other hand, his defense was ridiculous. I'm just saying there could be another side to that: he found himself in a greater number of long rallies, and in such a long match, because at times his offense was failing him.

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yeah, djoker wasn't at his best ; the very fact that he was missing quite a few shots when he went for it indicates a lower quality ...

rather than defense, I should've mentioned 'returning' ( getting back serves that in many cases would be forced errors of the return ), thus giving more chance for UEs in the rallies ...

one funny thing about a point you mentioned in that post : nadal @ wimbledon 2006, his forehand wasn't that good in the finals, fed's slice made him cough up quite a few errors, OTOH his BH was absolutely on fire and he blasted many winners and forced many errors from federer with it ...

^^ Well there's a small margin there for Djokovic, but it does align with the general view that he's top-ranked and a favorite to win.

Someone in another thread said that Ferrer played poorly (without belief), and that's suggested also in his negative AM. Djokovic and Ferrer, with their grinding styles, could be expected to produce low AM's when they meet; but in this case Djokovic's AM is quite high. So Ferrer's playing level does look genuinely low.

yeah, djoker wasn't at his best ; the very fact that he was missing quite a few shots when he went for it indicates a lower quality ...

rather than defense, I should've mentioned 'returning' ( getting back serves that in many cases would be forced errors of the return ), thus giving more chance for UEs in the rallies ...

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I am still very skeptical that higher quality of returns can produce lower AM's. It's a valid theory but I don't think there's good evidence for it -- and even in theory, a lot of things have to fall exactly into place for better returning to produce lower AM's.

First of all, if someone is producing quality service returns in the sense that he's cutting down on his unforced errors on the return, then that will immediately raise the AM's. So in theory, when we're comparing two matches and saying that one match has low AM's because it featured better returning, we need the better returning NOT to manifest itself as fewer UE's on the return. It can only manifest as better returns on huge serves that are not normally returned. In other words, the player whom we're saying is doing the quality returning cannot be producing better returns on medium/slow serves that are sometimes dropped into the net or driven out (UE's); if the player is being more careful with such serves and putting them back into play, then he's cutting down on the UE's in the match and raising the AM's.

That, already, strikes me as an unusual situation: for a quality returner to manifest his better returning, not on easy serves, but on hard serves. I'm not saying it can't happen: sometimes you do see players who return better when they have pace to work with; but players who tend to dump off-pace serves into the net are not the kind of players we usually think of as quality returners; and Djokovic is certainly not one of those inferior returners.

Another thing that must happen is this: the superior returner gets these tough serves back into play and the resulting rallies end to a significant degree in unforced errors. That again does not strike me as likely, because if a receiver somehow gets his racquet on a humongous serve and drives it back, when the server expected to see a weak return or no return at all, it's very likely that the server will be forced into an error. Djokovic does that countless of times to his opponents (just like Connors used to do).

It's true that Murray sometimes barely gets his racquet on the ball and his return floats softly, and deep, just inside the opposite baseline; and then a long rally ensues which sometimes ends in an UE. But Djokovic's superior returning very often manifests itself as a forcing return that shocks the server or throws him off balance and forces him into an error. And even when the server is not forced into an error and manages to scoop the ball back up, Djokovic at that stage is very often in a position to put away the next ball, or to force an error.

Superior returning off BIG, tough serves CAN end up in unforced errors at the end of the rally but very often it doesn't work that way.

When we tested this theory in the Djokovic/Murray/Fed matches last summer in the last two rounds at Wimbledon, you argued that Murray returned better than Djokovic and put more balls back into play, thus presenting more opportunities for UE's. But you saw my calculations: the number of extra balls that Murray put back in play cannot have resulted in more than 2 or 3 extra UE's, if that.

Additionally, you counted UE's on the return in both matches, and you found Murray making fewer of those errors than Djokovic did. That makes a lot of sense, given Murray's style of returning and style of play in general. But if that's the case -- if Murray returned better than Djokovic in those matches and the quality of Murray's returns manifested as fewer UE's -- then that just about the settles the question in my mind. Murray's superior returning, in the final, was REDUCING the number of UE's in that match, and raising the AM's. So if the final has lower AM's than the semifinal between Fed/Djokovic, we need to find some cause other than Murray's superior returning.

Brignacca gives us the following data from the 2005 Australian Open: In 127 matches charted, the average match winner AM was 22.5% and the average loser's AM was 11.0%.

I've only charted the AMs for the top 10 seeds plus a couple of potential spoilers (Raonic, Tomic) and Chardy, who made a run to the quarters. (I'm leaving out Monfils, as he's the outlier of outliers.) Here are the average AMs for the winners of all matches in the table and the average AMs of all losers of those matches:

Average AM of match winners: 23.2%

Average AM of match losers: 8.5%

So the these are pretty close to the 2005 averages. Since the wins were all posted by top 10 players or future top-10 players (Tomic & Raonic), we would expect the winning average to be greater than the whole-tournament winner's average from 2005, since that figure included many more early round victories posted by lower ranked players. The losses were distributed through the full seven rounds, but included the losses of 11 of the 12 quality players here under consideration (excluding the champion of course), so we might have expected the loser's average to be a bit higher as a consequence. I would generally expect the seeds to go down with a fight and post higher-than-average AMs in defeat. But this was not the case at this tournament: only 6 of the 12 (Federer, Tsonga, DelPotro, Gasquet, Raonic and Tomic) posted AMs greater than 10.0 in defeat. Interestingly, 4 of those men lost to Federer, which would seem to support the widespread pre-tournament view that he had a tough draw.

There was some talk at this tournament that the surface played faster this year than in previous years. I would say that the average AMs here do not support this view. On the other hand, many of these matches were played at night, when the courts apparently play much slower, so that may have skewed the AMs, but I'm not going to bother trying to sort that out.

It looks like this chart predicts that Djokovic will win in the finals, by about 8%.

Interesting.

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Yeah, based on this small sampling of data, it would appear that AMs might be useful as a predictor of victory in the later rounds of a tournament. Of course, a player could always bring out their best form after struggling through early rounds and blow the whole thing up, but that kind of thing can't be predicted by any other contrivance or art that I'm aware of.

I think I have to go back to what I said in one of the earlier posts (I forget which one). If a player increases his level of play, it's hard to imagine him not cutting down on his UE's.

With the other kinds of points -- the winners and forced errors -- there's a kind of logic to arguing that the defender, by raising his level, will offset the more successfully aggressive play of his opponent. You give as good as you get.

Not saying I agree that that could happen, but I see where you're coming from.

With the UE's, though, it's different. Those are the kind of errors that have least to do with what your opponent is doing. Those are the kind that you make when your concentration breaks momentarily; or you get physically lazy or something; or you've got a relatively simple shot but because you have a slight flaw in your technique you miss it.

I think we all agree that there are different kinds of UE's, and that sometimes an error is marked down as unforced even when the player commits it after a long, exhausting rally. On those points you could say that your opponent has a lot to do with your error.

But let's leave those ambiguous points aside. I'm talking about the most basic errors in a match: the ones that are entirely due to yourself. Every match has those. No one can play a perfect match.

And if the two players have genuinely raised their level, I can't see how they would not cut down on those types of errors.

I would expect those types of errors to decrease first and foremost, when you're playing well.

Anyway, once the UE's decrease, the AM's increase.

Still can't see how increased level of play can fail to raise AM's -- though it's still an interesting question!

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The scenario that I proposed seems to be logical (if the conditions outlined are fulfilled, the level of play may increase without changing the AM values of both players).

Is this scenario very realistic? I don't think so, however I do not find it completely unrealistic either.

As you have already mentioned sometimes quality rallies may end in an unforced error, although usually the number of UEs is reduced when the quality of play goes up. So the quality of play is in some way reflected by the AM's, however this relationship isn't straighforward. Actual values of the AM's are also shaped by these hypothetical situations (involving winners, forced errors and unforced errors) that I outlined in my scenario.

Perhaps the AM's are match-up sensitive? If this is the case the AM's may provide a convenient tool to compare matches played by the same opponents on the same or similar surface.

In 2008 they made the switch from Rebound Ace to Plexicushion. I am not sure but I have heard that Plexicushion is slower.

The AM's in '11 are lower than in '08, which is one piece of evidence that the Plexicushion itself was slowed down during the intervening years.

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It's difficult to figure out exactly what court surface they are using and what speed it is. The companies that make Rebound Ace and Plexicusion each make several different products of various speeds that each carry the Rebound Ace or Plexicusion branding. From the ITF court pace classification page:

"Plexipave" refers to the acrylic surface itself while "Plexicushion" refers to the EPDM rubber sub-surface. Here are the three Plexipave top surfaces marketed by the company, from their website:

Plexipave IW - ITF Category 1 - Pace: Slow
For those who desire a much slower surface, to compensate for lower humidity, high altitudes or simply to change the pace of the game, Plexipave has developed the I.W. mixture, first used at the Indian Wells, CA tournament facility.

Plexipave Standard - ITF Category 3 - Pace: Medium
Considered by many to be the best combination of consistency-of-play, pace and foothing. Plexipave Standard is the traditional and most widely used tennis court surface system. Standard Plexipave provides a consistent and reliable medium-pace playing surface.

Plexipave H.U. - ITF Category 4 - Pace: Medium-Fast
Harvard University has been the birthplace of many great innovations and playing traditions. Plexipave H.U. is no exception. It has also been adapted as the standard for the Australian Open Series.

So according to Plexipave, Plexipave H.U. has been adopted as the standard for the Australian Open series.

So according to Plexipave, the AO surface is a Plexipave H.U. acrylic topcoat over a Plexicushion Prestige subsurface. Both of these products are classified by ITF as "Medium-Fast" surfaces. The press, however, has consistently described the surface at the AO as "Medium". In short, there is no way of knowing if the courts are faster or slower from one year to the next without somebody in the know doing the telling.

For each year, for Murray’s first six matches, I compared his aggressiveness with that of his opponents in two ways. To check how successful he was at hitting big shots compared to his opponents, I added up his winners and his opponents’ forced errors — mistakes they made as a result of Murray shots — and compared those with the sum of his opponents’ winners and his forced errors. Then, I compared Murray’s unforced errors with his opponents’; if he was playing more aggressively, he should also be ending more of the points he loses with his own racket than his opponents, or at least more than he used to.

The stats suggest that not much has changed. In 2011, Murray won 21.3% more points with his racket than his opponents did in his first six matches. That dipped to 20% last year, and rose to 22.5% this year — slight blips, but not a significant shift. Meanwhile, the unforced-errors stats suggest he hasn’t gotten much more willing to accept risk. In 2011, he hit 36% fewer unforced errors in his first six matches than his opponents did. Last year, that figure fell to 21.4% — Murray was losing more points with his aggression than he used to, though still fewer than his opponents did. But this year Murray has lost 34.1% fewer points to unforced errors than his opponents have, indicating he is again winning lots of points by playing less risky tennis than his opponents.

Thanks. I'll have to go back and watch that one. Haven't seen it in over six years

Do you think it was immediately after that match that Toni and Rafa resolved to attack the slice mercilessly? Nowadays, Rafa seems utterly committed to attacking the slice with the forehand whenever he sees it, and with the spin he can produce he can rip the short slice up over the net and into a corner like no one else. He's nearly eliminated that shot from Roger's arsenal when they play, further torturing Fed's backhand side. I also remember reading a piece by Steve Tignor in which he relates walking by a practice court at Indian Wells and seeing Rafa ripping backhands off short slices too (this was maybe 3-4 years ago). The domination of your backhand is now complete, no?

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heh, not really sure ..... people talk about the rafa FH high up to fed's BH all the time, but rafa just ripping apart those slices unless they are absolute top notch is just as important factor ...

I am still very skeptical that higher quality of returns can produce lower AM's. It's a valid theory but I don't think there's good evidence for it -- and even in theory, a lot of things have to fall exactly into place for better returning to produce lower AM's.

First of all, if someone is producing quality service returns in the sense that he's cutting down on his unforced errors on the return, then that will immediately raise the AM's. So in theory, when we're comparing two matches and saying that one match has low AM's because it featured better returning, we need the better returning NOT to manifest itself as fewer UE's on the return. It can only manifest as better returns on huge serves that are not normally returned. In other words, the player whom we're saying is doing the quality returning cannot be producing better returns on medium/slow serves that are sometimes dropped into the net or driven out (UE's); if the player is being more careful with such serves and putting them back into play, then he's cutting down on the UE's in the match and raising the AM's.

That, already, strikes me as an unusual situation: for a quality returner to manifest his better returning, not on easy serves, but on hard serves. I'm not saying it can't happen: sometimes you do see players who return better when they have pace to work with; but players who tend to dump off-pace serves into the net are not the kind of players we usually think of as quality returners; and Djokovic is certainly not one of those inferior returners.

Another thing that must happen is this: the superior returner gets these tough serves back into play and the resulting rallies end to a significant degree in unforced errors. That again does not strike me as likely, because if a receiver somehow gets his racquet on a humongous serve and drives it back, when the server expected to see a weak return or no return at all, it's very likely that the server will be forced into an error. Djokovic does that countless of times to his opponents (just like Connors used to do).

It's true that Murray sometimes barely gets his racquet on the ball and his return floats softly, and deep, just inside the opposite baseline; and then a long rally ensues which sometimes ends in an UE. But Djokovic's superior returning very often manifests itself as a forcing return that shocks the server or throws him off balance and forces him into an error. And even when the server is not forced into an error and manages to scoop the ball back up, Djokovic at that stage is very often in a position to put away the next ball, or to force an error.

Superior returning off BIG, tough serves CAN end up in unforced errors at the end of the rally but very often it doesn't work that way.

When we tested this theory in the Djokovic/Murray/Fed matches last summer in the last two rounds at Wimbledon, you argued that Murray returned better than Djokovic and put more balls back into play, thus presenting more opportunities for UE's. But you saw my calculations: the number of extra balls that Murray put back in play cannot have resulted in more than 2 or 3 extra UE's, if that.

Additionally, you counted UE's on the return in both matches, and you found Murray making fewer of those errors than Djokovic did. That makes a lot of sense, given Murray's style of returning and style of play in general. But if that's the case -- if Murray returned better than Djokovic in those matches and the quality of Murray's returns manifested as fewer UE's -- then that just about the settles the question in my mind. Murray's superior returning, in the final, was REDUCING the number of UE's in that match, and raising the AM's. So if the final has lower AM's than the semifinal between Fed/Djokovic, we need to find some cause other than Murray's superior returning.

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actually , by my stats

32 UEs in 133 rallies in the semi (24.06%)
49 UEs in 206 rallies in the final (23.8%)

having said that murray's superior returning on the first serves doesn't seem to have as much of an effect on the no of UEs as I initially thought ....

perhaps better returning of 1st serves has more of an effect on slower surfaces where % of UEs per no of baseline rallies is more !?

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Yes, since you gave more UE's to the semifinal than Wimbledon.com did, your AM's for the two matches are already very close. And the AM's would be even closer in the hypothetical scenario in which Murray returns only as well as Djokovic did, and we drop 5 UE's from the final -- but I think there are a few problems with that last step.

In your stats Murray made 4 fewer UE's on the return than Djokovic did. And if we're asking how many of the total UE's in the match resulted from Murray's superiority over Djokovic as a returner, those 4 fewer UE's have to be accounted for.

So if Murray's extra returns in play added 5 UE's to the final, his returning also took away 4 UE's. For all intents and purposes that cancels out any effect on the AM's, as far as Murray's extra returns go.

And the UE's that Murray avoided making on 4 points, at least in your count, are certain; the 5 UE's that he added over the course of the match by getting extra returns in play are hypothetical. Most of those extra returns would have been on serves that normally caused forced errors, rather than UE's (that has to be true because the vast majority of the return errors in the match, by anyone's count, were forced).

So I go back to the arguments I made above. If the receiver gets a tough, forcing serve back into play, a common result is for the server to be shocked or thrown off balance, and forced into an error. We're extrapolating our UE's based on the total % of rallies that ended in UE's, but a rally that starts with a tough serve unexpectedly returned is not a typical rally. The % of such rallies that end in UE's could be very different from the overall %.

So the 'extra' UE's produced by Murray's returning could be 5, or perhaps only 2 or 3. And Murray avoided making UE's himself on 4 returns: so I think even going with your numbers it's a very difficult argument to make, that better returning can produce lower AM's.

As far as slower surfaces, as you say, the % of UE in rallies is larger. So hypothetically a receiver who gets a lot of tough first serves back into play can end up inflating the total number of UE's in the match.

However, the same objection there: on slow surfaces, serves do not force errors the way they do on fast surfaces. And the players themselves don't necessarily serve all-out the way they do on fast surfaces. There are more opportunities to make UE's on the return. So a player who displays superior returning skills should also be reducing the UE's in a match when he gets easy/moderate serves back into play, thus raising the AM's.

Yes, since you gave more UE's to the semifinal than Wimbledon.com did, your AM's for the two matches are already very close. And the AM's would be even closer in the hypothetical scenario in which Murray returns only as well as Djokovic did, and we drop 5 UE's from the final -- but I think there are a few problems with that last step.

In your stats Murray made 4 fewer UE's on the return than Djokovic did. And if we're asking how many of the total UE's in the match resulted from Murray's superiority over Djokovic as a returner, those 4 fewer UE's have to be accounted for.

So if Murray's extra returns in play added 5 UE's to the final, his returning also took away 4 UE's. For all intents and purposes that cancels out any effect on the AM's, as far as Murray's extra returns go.

And the UE's that Murray avoided making on 4 points, at least in your count, are certain; the 5 UE's that he added over the course of the match by getting extra returns in play are hypothetical. Most of those extra returns would have been on serves that normally caused forced errors, rather than UE's (that has to be true because the vast majority of the return errors in the match, by anyone's count, were forced).

So I go back to the arguments I made above. If the receiver gets a tough, forcing serve back into play, a common result is for the server to be shocked or thrown off balance, and forced into an error. We're extrapolating our UE's based on the total % of rallies that ended in UE's, but a rally that starts with a tough serve unexpectedly returned is not a typical rally. The % of such rallies that end in UE's could be very different from the overall %.

So the 'extra' UE's produced by Murray's returning could be 5, or perhaps only 2 or 3. And Murray avoided making UE's himself on 4 returns: so I think even going with your numbers it's a very difficult argument to make, that better returning can produce lower AM's.

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well, the receiver being forced into error when a RoS is made on a medium-tough serve is one scenario .... but the same scenario is applicable on other kind of serves ....

it could be that on a medium to tough serve, the return is 'neutral' and ensuing rally may result in a UE ..

either way, I really don't think there is a 'significant' difference in those sort of returns ..

one thing that you are probably neglecting is that when someone returns so many of those first serves, it puts quite a bit of pressure of the server; who'd most probably be forced to go for more and commit more UEs ....

that is more common than someone making careless UEs even while getting quite a free points on the serve

@ the bold part, could be .... but one another thing is the point I've made above ....

As far as slower surfaces, as you say, the % of UE in rallies is larger. So hypothetically a receiver who gets a lot of tough first serves back into play can end up inflating the total number of UE's in the match.

However, the same objection there: on slow surfaces, serves do not force errors the way they do on fast surfaces. And the players themselves don't necessarily serve all-out the way they do on fast surfaces. There are more opportunities to make UE's on the return. So a player who displays superior returning skills should also be reducing the UE's in a match when he gets easy/moderate serves back into play, thus raising the AM's.

Click to expand...

yeah, fair point ... might actually want to apply this on a couple of examples to really 'test' this ....again the point I've made in the first part is applicable here as well ...

A good piece on the Tsonga-Federer match, from The Daily Fix blog at WSJ:

Djokovic’s Many Happy Returns.

By Carl Bialik

Jo-Wilfried Tsonga’s serve looked unbreakable for most of his Wimbledon quarterfinal upset of Roger Federer on Wednesday. Two days later, Tsonga was broken six times by Novak Djokovic, who claimed the No. 1 ranking and his first Wimbledon final berth with the win. The difference is mostly due to Djokovic’s superior return game, the best in tennis. But it also reflects the importance of winning points at the right time, something Federer didn’t do against Tsonga but Djokovic did.

In two days, Jo-Wilfried Tsonga’s serve devolved from extraordinary to ordinary.Federer won 29% of points in Tsonga’s service games, compared to 39% for Djokovic. That may sound like a moderate difference, but it turns out to be enormous. Breaking serve requires winning four return points, or more, in the same game and outscoring the server by at least two points. So any small edge in returning on any point accumulates over the course of a game. If Federer had the same 29% chance of winning any particular point in Tsonga’s service games, then he had a 9% chance of breaking in each of those games. Djokovic’s chance, assuming his probability of winning any Tsonga service point was 39%, was 25% — nearly three times as great as Federer’s. That means Federer could have expected to break Tsonga twice, and Djokovic five times (Tsonga had more service games in his five-setter against Federer than in his four sets against Djokovic). The actual numbers were close: One and six, respectively.

But on grass, where big servers often thrive and one break can be enough to win a set, Federer’s inability to get that second break may have prevented him from winning the match, while Djokovic’s extra break helped him close out Tsonga in four. The discrepancies reflect that Djokovic clustered his return points well: Tsonga had some easy service games against him, but Djokovic dominated him in others. Federer, instead, consistently scored one or two points on most Tsonga service games but never even had another break point after breaking Tsonga in Tsonga’s first service game. Given the number of return points he won, if Federer had clustered them randomly he could have expected to hold at least one break point in six different Tsonga service games. His probability of holding a break point in just one (or none) was 1%, yet that’s what happened. Tsonga, against Federer, clustered his return points well — he won just 24% of his and could have expected just one service break. Instead he broke three times and beat Federer, despite losing 10 more points than he won.

Sadly for Federer, this has become the norm at the tournament he once owned. This is the fourth straight Wimbledon in which he broke just once in his final match at the tournament. In 2009, that break was enough to beat Andy Roddick in five sets. But in the 2008 final against Rafael Nadal and in Federer’s 2010 quarterfinal against Thomas Berdych, one break didn’t suffice. And each time, Federer had fewer breaks than would be expected from the proportion of return points he won. Against Berdych he should have had three; against Roddick, three; and against Nadal, four. This is a result of Federer’s recent record of poor rates of break-point conversions in big matches at majors, but also of too many games in which he never quite got to break point. If Federer wants to beat the likes of Tsonga next year, as well as Djokovic and Nadal, he’ll have to find a way to pack his return points into single games, and make the most of them.​

I've made several additions to the lists for the players above; Roddick's has changed the most. The best I had for him previously was his 2009 Wimbledon victory over Murray; there are now 8 performances higher than that, most of them from the 2003-05 period.

In the last ten years I've got Federer, Nadal, Murray, Mahut, Gonzalez and now Roddick breaking the 40% mark. Of those, only Federer, Nadal and Gonzalez have broken that mark on something other than grass.

I've made several additions to the lists for the players above; Roddick's has changed the most. The best I had for him previously was his 2009 Wimbledon victory over Murray; there are now 8 performances higher than that, most of them from the 2003-05 period.

Click to expand...

Very interesting stats, thanks for taking the time to get them up here.

Tsonga would have had the AM edge if he'd won more points overall, but he trailed in total points by 136-146.

Despite the pressure on his serve, Federer still managed to win 78% of his 1st serve points, compared to Tsonga's 73%. And on second serve Federer also led, 71% to 67%.

The reason Tsonga won the match while winning fewer points overall is that he converted 3 break points while Federer converted only one.

In other words Tsonga was better than Federer on the most important points (the break points).

Click to expand...

given fed had only one breakpoint, he surely couldn't convert more than one ?

tsonga went for it in the early stages of each set in set 3, 4 and 5 and got a break each , but otherwise, he was winning very few points on fed's serve ... fed was getting more times into 30, 40 on tsonga's serve, but couldn't get to BPs .... his return was sorely lacking and he was pretty passive from the ground ...

A good piece on the Tsonga-Federer match, from The Daily Fix blog at WSJ:

Djokovic’s Many Happy Returns.

By Carl Bialik

Jo-Wilfried Tsonga’s serve looked unbreakable for most of his Wimbledon quarterfinal upset of Roger Federer on Wednesday. Two days later, Tsonga was broken six times by Novak Djokovic, who claimed the No. 1 ranking and his first Wimbledon final berth with the win. The difference is mostly due to Djokovic’s superior return game, the best in tennis. But it also reflects the importance of winning points at the right time, something Federer didn’t do against Tsonga but Djokovic did.

In two days, Jo-Wilfried Tsonga’s serve devolved from extraordinary to ordinary.Federer won 29% of points in Tsonga’s service games, compared to 39% for Djokovic. That may sound like a moderate difference, but it turns out to be enormous. Breaking serve requires winning four return points, or more, in the same game and outscoring the server by at least two points. So any small edge in returning on any point accumulates over the course of a game. If Federer had the same 29% chance of winning any particular point in Tsonga’s service games, then he had a 9% chance of breaking in each of those games. Djokovic’s chance, assuming his probability of winning any Tsonga service point was 39%, was 25% — nearly three times as great as Federer’s. That means Federer could have expected to break Tsonga twice, and Djokovic five times (Tsonga had more service games in his five-setter against Federer than in his four sets against Djokovic). The actual numbers were close: One and six, respectively.

But on grass, where big servers often thrive and one break can be enough to win a set, Federer’s inability to get that second break may have prevented him from winning the match, while Djokovic’s extra break helped him close out Tsonga in four. The discrepancies reflect that Djokovic clustered his return points well: Tsonga had some easy service games against him, but Djokovic dominated him in others. Federer, instead, consistently scored one or two points on most Tsonga service games but never even had another break point after breaking Tsonga in Tsonga’s first service game. Given the number of return points he won, if Federer had clustered them randomly he could have expected to hold at least one break point in six different Tsonga service games. His probability of holding a break point in just one (or none) was 1%, yet that’s what happened. Tsonga, against Federer, clustered his return points well — he won just 24% of his and could have expected just one service break. Instead he broke three times and beat Federer, despite losing 10 more points than he won.

Sadly for Federer, this has become the norm at the tournament he once owned. This is the fourth straight Wimbledon in which he broke just once in his final match at the tournament. In 2009, that break was enough to beat Andy Roddick in five sets. But in the 2008 final against Rafael Nadal and in Federer’s 2010 quarterfinal against Thomas Berdych, one break didn’t suffice. And each time, Federer had fewer breaks than would be expected from the proportion of return points he won. Against Berdych he should have had three; against Roddick, three; and against Nadal, four. This is a result of Federer’s recent record of poor rates of break-point conversions in big matches at majors, but also of too many games in which he never quite got to break point. If Federer wants to beat the likes of Tsonga next year, as well as Djokovic and Nadal, he’ll have to find a way to pack his return points into single games, and make the most of them.​

well, the receiver being forced into error when a RoS is made on a medium-tough serve is one scenario .... but the same scenario is applicable on other kind of serves ....

it could be that on a medium to tough serve, the return is 'neutral' and ensuing rally may result in a UE ..

either way, I really don't think there is a 'significant' difference in those sort of returns ..

Click to expand...

A number of things could happen when a tough serve is barely returned. The return could land softly but so deep that a neutral rally ensues. Or it could land in such a way that the server gets a chance to rip the floater for a winner or a forced error. Or the return could surprise the server and put him off balance, making it more likely that the receiver will rip a winner or force an error.

I don't know which of those scenarios is really more applicable to the kind of serves which we think Murray returned successfully and Djokovic unsuccessfully. Not sure we can go any further with this.

one thing that you are probably neglecting is that when someone returns so many of those first serves, it puts quite a bit of pressure of the server; who'd most probably be forced to go for more and commit more UEs ....

Click to expand...

This is different from the scenario we've been talking about. We've been debating your initial suggestion that because Murray got a great number of serves back in play, there were more rallies in the final compared to the SF -- hence more UE's and lower AM's.

What you're suggesting here is simply that good play by one opponent can result in poorer play by the other. That's not controversial at all; I'd agree with that. If the server, finding his serves always popping back at him, starts to go for too much and makes more UE's, his AM will go down; while the receiver's AM will go up, since he's making so few UE's on the return.

But that's different from the claim that both players' AM's are going down due to the receiver putting so many serves back in play. That IS debatable, because it means that AM's can go down even when quality of play (in this case, quality of returning) goes up. That's very different from merely observing that one guy's good play can make the other guy fall into errors.

Sampras lost the final to Agassi in 3 straight sets with an AM of only 15.5%, compared to Agassi's 25.5%.

A report in the press on the Sampras-Rafter QF which Pete won 4-6, 7-6, 6-4.

Playing matches of the quality of his 4-6 7-6 6-4 quarter-final victory over Patrick Rafter at the Tennis Masters Series-Indian Wells is what keeps tennis fun for Pete Sampras after all the years and so much success.

"It was a highly competitive match today. It was good tennis," the third-seeded Sampras said."(It) felt like it brought back my memories to Wimbledon last year," he said of the classic final against Rafter that brought Sampras his record 13 Grand Slam title.

"If I would have walked off there losing, I would have felt pretty good considering the way he played," Sampras said. "When you have stats like that, you can always say it's a high level of tennis."

In the hunt for his first title of the year, Sampras pounded 47 winners against only seven unforced errors, while Rafter had 40 winners and 14 unforced errors. "People enjoyed it. It was fun to be a part of it. Of course, I'm more happy that I got through it and won it," Sampras said of the two hour and 12 minute tussle that could well have been his best played match of the year.

Both Sampras and Rafter rely on an aggressive serve-and-volley style of play, but the former world number one had the edge from the service line.

"He serves very well, and when you serve that big you can take big swings on returns and that's where he does very well," Rafter said. "He's going to break you sooner or later. He's not the best returner in the world, but he is the best server in the world. He returns solid enough and consistently enough to break you."

After taking the second set, Sampras, the 1994 and '95 champion here, reeled off the first nine points of the third set, breaking Rafter early. He never offered the the 11th-seeded Rafter a chance to return the favour in the final set, only reaching deuce once on any of his service games.
​

Unforced Error Is Unloved Statistic Among Tennis Players
By BEN ROTHENBERG
INDIAN WELLS, Calif. — The term unforced error has become a staple of the popular vernacular since its introduction in tennis three decades ago. And though the phrase is still largely identified with the sport, players and coaches have little regard for the statistic. Nor do they care much for the statistical identification of shots as winners or unforced errors, considering them misleading reflections of the flow of a match.

Andy Murray, the defending United States Open champion, said he looked for only one thing on a postmatch stats sheet.

“The most important one is if there’s a W next to your name,” he said. “The rest you can pretty much throw out.”

But the statistics persist, probably because fans find them meaningful.

Leo Levin, director of product development for the analytics company Information and Display Systems, helped coin the term unforced error when he was developing the first computerized tennis statistics system in 1982 as a coaching aid. Every point was classified as ending in either a winner, a forced error or an unforced error.

“We had the concept of a shot that is ‘forcing’ or just ‘in-play,’ ” Levin said. “So if players are trading what we consider to be ‘in-play’ or neutral shots, a resulting error would have to be unforced.”

Though a winner (a shot that lands in the court and is not touched by the opponent) is easy to determine, deciding whether an error is forced or unforced is subjective. And when more than one statistician is working a match — usually one for the tournament and one for the broadcaster — their totals can differ drastically.

According to Information and Display Systems, a player commits an unforced error if he does not keep a ball in play though he is not “under any physical pressure as a result of the placement, pace, power or spin of their opponents stroke.”

Information and Display Systems runs video training sessions with its statisticians to work toward as much unanimity as possible in classifying errors, but making it an exact science may be impossible.

“I think if you have two or three different people recording unforced errors, you’re going to get two or three different figures,” said Kevin Fischer, senior communications manager for the Women’s Tennis Association. “One person is going to see a person that’s constructed a point, a long rally, and a player then hits it into the net — is it forced or unforced? Totally the call of the person behind the computer.”

Levin contends that unforced errors are a more revealing statistic for assertive players who can become erratic.

“You’ll see that a lot of times when a player like Serena Williams loses a match,” he said. “It’s not usually because she got overpowered; she was the aggressor, but she was making mistakes. So unforced errors are typically a key factor for her when she loses. But when she wins, she’s not winning because her opponents are making mistakes, she’s winning because she’s dominating by forcing mistakes and hitting winners.”

Statistics on winners and unforced error counts are commonly reported by the news media, but forced errors are not, even though their inclusion could, at least for fans, provide a more complete representation of the flow of a match.

In her third-round loss at the 2013 Australian Open, the British teenager Laura Robson hit 6 winners and 29 unforced errors, which would make her performance seem woefully erratic. But Robson also forced 19 errors from her opponent, Sloane Stephens, thus assertively claiming points without hitting clean winners.

“Unforced errors and winners are more glamorous,” Levin said. “They’re easier to spot; there’s more of a story there a lot of the time. And one of the things we learned as we developed the stats, especially as you deal with media and broadcasters: they’re trying to paint pictures; they’re trying to tell stories.

“And it’s easier to tell a story with ‘He made 20 unforced errors; he’s giving away a lot of points.’ You can articulate that really easily. Or if he’s hitting a lot of winners, it’s flashy shots. Again, it creates a buzz. But if you talk about ‘He’s forcing a lot of mistakes,’ it doesn’t have the same appeal.”

Though the system of classifying point-ending shots was developed for coaches, many of them, and players, like Murray, disavow the statistics.

“Having worked in the N.B.A., you have TV timeouts and the first thing the coaches want is the box score,” Fischer said.

He added: “Here, they sit at a changeover and you flash up the first-set stats, and they completely ignore it. They don’t look.”

Sam Sumyk, who coaches the world No. 2 Victoria Azarenka, said statistics were misleading.

“I’m not interested on the statistics, because I’m not sure it’s accurate,” Sumyk said. “So I rather go see by myself, and see with my own eyes, and make my opinion or judgment.”

Many top players seem to agree with his assessment.

“The forced error, unforced error count is always extremely tricky,” said Roger Federer, who has won 17 Grand Slam tournaments. “I know, and my coaches know, what happened during the match, so I don’t necessarily need stats to point out things.”​

About a year ago I had an idea that turned out to be similar to the AM, and opened a thread http://tt.tennis-warehouse.com/showthread.php?t=412175
analyzing Nadal’s last 7 slam finals up to that point. Then I was reminded by Moose Malloy that a similar concept already existed and was called the Aggressive Margin. I later learned that the inventor of the concept is a statistician named Bill Jacobson.

But I still think it is more useful to break down the AM number into its two components the way I did in that thread, mainly because it allows you to see much better why a match was won.

To illustrate, take these two Berdych-Nadal matches that I looked at in that thread (the phrase “points forcibly won” means “points won by anything other than UEs from the opponent”).

Nadal-Berdych, AO 2012
Points forcibly won as percentage of total points played
Nadal 33%
Berdych 38%
Total 72% (rounded)

UEs made as percentage of total points played
Nadal 10%
Berdych 18%
Total 28%

Balance: Nadal 23, Berdych 20 [+3]

Now, this is what you may expect from such a matchup. Berdych with a higher ratio of “forcibly won” points, but Nadal overcoming the difference with a comparatively larger difference in the UE ratio.

Then consider the following match between the same pair of players.

Nadal-Berdych, Wimbledon 2010
Points forcibly won as percentage of total points played
Nadal 44%
Berdych 33%
Total 77%

UEs made as percentage of total points played
Nadal 12%
Berdych 10%
Total 22%

Balance: Nadal 32, Berdych 23 [+9]

This is interesting in the sense it runs counter to what one might expect from such a matchup. Nadal’s higher AM in this match comes entierly from the aspect of the game where you’d expect Berdych to do a bit better, and Nadal actually has a slightly higher rate of UEs than Berdych – certainly not what one would expect.

In general, it appears that the player with the higher ratio of forcibly won points most often wins, but not always.

I suppose the final AM balance is almost always a very reliable predictor of who won the match. Exceptions must be extremely rare, though they may occur by differences in the outcome of a few "key points". When they occur, you could justifiably say that the better player lost.

In addition to helping us see why a match was won, breaking the AM number down into its two components also allows a quick assessment of the relative quality between two matches (provided it’s the same surface) by showing the total UE ratio in the match. In the above case of course it doesn’t really do that because we are dealing with two different surfaces and you’d always expect a higher UE ratio on slower courts.

But the main point is that if one presents the information condensed in one pair of numbers 32-23, it doesn’t immediately allow you to see where the difference actually came from.

I also think that the winner’s level of play may not always be reliably derived from his AM alone, because, by itsef, this number doesn't tell you the opponent’s level of play. What I mean is, if the opponent is for example feeding you lots of easy balls, you’ll end up with a high AM, but not necessarily from a higher level of play than in another match with a lower AM but a better opponent who makes things more difficult for you.

Nadal-Berdych, Wimbledon 2010
Points forcibly won as percentage of total points played
Nadal 44%
Berdych 33%
Total 77%

UEs made as percentage of total points played
Nadal 12%
Berdych 10%
Total 22%

Balance: Nadal 32, Berdych 23 [+9]

This is interesting in the sense it runs counter to what one might expect from such a matchup. Nadal’s higher AM in this match comes entierly from the aspect of the game where you’d expect Berdych to do a bit better, and Nadal actually has a slightly higher rate of UEs than Berdych – certainly not what one would expect.

Click to expand...

That match is a bit unusual because Nadal had more UE's than his opponent, which is almost always not true. Nadal ended up with an inferior winner/error differential (+8 compared to Berdych's +10), which is also unusual; when Nadal wins his matches he typically has a better winner/error differential than his opponent.

It could just be a quirk of the stats, or something of greater significance, I'm not sure.

They also met at Wimbledon in '07. Nadal had fewer UE's than Berdych in that one (20 vs 30). But just as in the 2010 match, he won more points than Berdych with forcing plays (winners + shots that force errors). In the '07 match as a whole, 41% of the points were ended by Nadal's forcing plays, only 32% by Berdych's.

So maybe there's something unusual about the way these two players match up.

In general, it appears that the player with the higher ratio of forcibly won points most often wins, but not always.

Click to expand...

I doubt that this is true. In all of Agassi's wins over Sampras for which I have the AM's calculated, Agassi won fewer points with forcing plays than Sampras did. Agassi had the higher AM, of course, because his UE's were lower than Sampras'. But the forcing plays more often came from Sampras, because that was his style.

I have AM's calculated for most of the Nadal/Federer matches, and it's the same thing there. Federer makes more forcing plays than Nadal almost every time: the two exceptions I have are the 2008 RG final and the recent QF at Indian Wells.

In the Indian Wells match it is very close. By a very small margin (34% vs 32%), more points in the match ended with Nadal's forcing plays than with Federer's.

In the RG match it's 40% vs 31%.

But these were absolute blowouts for Nadal. Only when he beats his opponent comprehensively does Nadal end up with the higher number of forcing plays.

I suppose the final AM balance is almost always a very reliable predictor of who won the match. Exceptions must be extremely rare, though they may occur by differences in the outcome of a few "key points". When they occur, you could justifiably say that the better player lost.

Click to expand...

Yes the AM almost always indicates correctly who won the match, since the higher AM always goes to the player who won more total points. The few exceptions would be those cases where the loser of the match wins more points than his opponent (cases where the better player lost as you say).

Just a general point: I agree that breaking up the AM as you have does tell you more about what happened in the match.

Serena beat Radwanska yesterday in Miami with 40 winners in only 15 games played (6-0, 6-3). But as impressive as her performance was, she also had 21 unforced errors, so her AM was not one of her highest (40 winners against 21 UE is excellent but not one of the alltime best, which would be those performances with UE's in the single digits).

Originally Posted by Benhur
In general, it appears that the player with the higher ratio of forcibly won points most often wins, but not always.

Click to expand...

Originally Posted by krosero
I doubt that this is true. In all of Agassi's wins over Sampras for which I have the AM's calculated, Agassi won fewer points with forcing plays than Sampras did. Agassi had the higher AM, of course, because his UE's were lower than Sampras'. But the forcing plays more often came from Sampras, because that was his style.

I have AM's calculated for most of the Nadal/Federer matches, and it's the same thing there. Federer makes more forcing plays than Nadal almost every time: the two exceptions I have are the 2008 RG final and the recent QF at Indian Wells.

In the Indian Wells match it is very close. By a very small margin (34% vs 32%), more points in the match ended with Nadal's forcing plays than with Federer's.

In the RG match it's 40% vs 31%.

But these were absolute blowouts for Nadal. Only when he beats his opponent comprehensively does Nadal end up with the higher number of forcing plays.

Click to expand...

You are probably right. But remember I was just making that assessment based on a very small sample of 7 matches, where 71% of them were won by the more aggressive player. It may well be that the actual ratio in a large sample could be close to 50-50.

About a year ago I had an idea that turned out to be similar to the AM, and opened a thread http://tt.tennis-warehouse.com/showthread.php?t=412175
analyzing Nadal’s last 7 slam finals up to that point. Then I was reminded by Moose Malloy that a similar concept already existed and was called the Aggressive Margin. I later learned that the inventor of the concept is a statistician named Bill Jacobson.

But I still think it is more useful to break down the AM number into its two components the way I did in that thread, mainly because it allows you to see much better why a match was won.

To illustrate, take these two Berdych-Nadal matches that I looked at in that thread (the phrase “points forcibly won” means “points won by anything other than UEs from the opponent”).

Nadal-Berdych, AO 2012
Points forcibly won as percentage of total points played
Nadal 33%
Berdych 38%
Total 72% (rounded)

UEs made as percentage of total points played
Nadal 10%
Berdych 18%
Total 28%

Balance: Nadal 23, Berdych 20 [+3]

Now, this is what you may expect from such a matchup. Berdych with a higher ratio of “forcibly won” points, but Nadal overcoming the difference with a comparatively larger difference in the UE ratio.

Then consider the following match between the same pair of players.

Nadal-Berdych, Wimbledon 2010
Points forcibly won as percentage of total points played
Nadal 44%
Berdych 33%
Total 77%

UEs made as percentage of total points played
Nadal 12%
Berdych 10%
Total 22%

Balance: Nadal 32, Berdych 23 [+9]

This is interesting in the sense it runs counter to what one might expect from such a matchup. Nadal’s higher AM in this match comes entierly from the aspect of the game where you’d expect Berdych to do a bit better, and Nadal actually has a slightly higher rate of UEs than Berdych – certainly not what one would expect.

In general, it appears that the player with the higher ratio of forcibly won points most often wins, but not always.

I suppose the final AM balance is almost always a very reliable predictor of who won the match. Exceptions must be extremely rare, though they may occur by differences in the outcome of a few "key points". When they occur, you could justifiably say that the better player lost.

In addition to helping us see why a match was won, breaking the AM number down into its two components also allows a quick assessment of the relative quality between two matches (provided it’s the same surface) by showing the total UE ratio in the match. In the above case of course it doesn’t really do that because we are dealing with two different surfaces and you’d always expect a higher UE ratio on slower courts.

But the main point is that if one presents the information condensed in one pair of numbers 32-23, it doesn’t immediately allow you to see where the difference actually came from.

I also think that the winner’s level of play may not always be reliably derived from his AM alone, because, by itsef, this number doesn't tell you the opponent’s level of play. What I mean is, if the opponent is for example feeding you lots of easy balls, you’ll end up with a high AM, but not necessarily from a higher level of play than in another match with a lower AM but a better opponent who makes things more difficult for you.

You are probably right. But remember I was just making that assessment based on a very small sample of 7 matches, where 71% of them were won by the more aggressive player. It may well be that the actual ratio in a large sample could be close to 50-50.

Click to expand...

Well actually I sorted my data tonight and it turns out most of my matches were won by the more aggressive player, ie, the one who made the greater number of forcing plays (winners + shots that force errors). That is the same thing you found. However, I also found out that most of my matches were won by the player who made fewer unforced errors.

The reason that's possible is that it's very common for both things to occur: the winner will make fewer unforced errors AND he will make the greater number of forcing plays.

I've got a total of 419 men's matches with AM's calculated.

77% of the matches were won by the player who made more forcing plays.

70% of the matches were won by the player who made fewer UE's.

In almost half of the matches (48%), the winner did both things: he made more forcing plays and he made fewer UE's.

From this data it looks as if you're slightly more likely to win a tennis match if you're an aggressive player making forcing shots, rather than a conservative player who makes few UE's.

However I think my data set is probably skewed toward matches with high numbers of winners, ie, aggressive play. That's because the data set began with a project by Moose and myself in which we were counting the number of winners made in a match (rarely counting the UE's); and we were deliberately looking for matches with high-winner counts. Those were the matches that caught our eye, so to speak.

Also, I did a ton of Becker matches at the start of the project just because I'm a fan of his. Moose is a fan of McEnroe and he did a lot of his matches. We both have done a lot of Lendl matches. All of these guys, needless to say, were aggressive players.

Over time we've systematically gone through matches just because they were GS finals or other important matches, so that would offset, to some degree, any bias toward matches with high-winner counts. But I think it's likely that in our database, "aggressive" style matches still outnumber the ones with "conservative" styles.

Well actually I sorted my data tonight and it turns out most of my matches were won by the more aggressive player, ie, the one who made the greater number of forcing plays (winners + shots that force errors). That is the same thing you found. However, I also found out that most of my matches were won by the player who made fewer unforced errors.

The reason that's possible is that it's very common for both things to occur: the winner will make fewer unforced errors AND he will make the greater number of forcing plays.

I've got a total of 419 men's matches with AM's calculated.

77% of the matches were won by the player who made more forcing plays.

70% of the matches were won by the player who made fewer UE's.

In almost half of the matches (48%), the winner did both things: he made more forcing plays and he made fewer UE's.

From this data it looks as if you're slightly more likely to win a tennis match if you're an aggressive player making forcing shots, rather than a conservative player who makes few UE's.

However I think my data set is probably skewed toward matches with high numbers of winners, ie, aggressive play. That's because the data set began with a project by Moose and myself in which we were counting the number of winners made in a match (rarely counting the UE's); and we were deliberately looking for matches with high-winner counts. Those were the matches that caught our eye, so to speak.

Also, I did a ton of Becker matches at the start of the project just because I'm a fan of his. Moose is a fan of McEnroe and he did a lot of his matches. We both have done a lot of Lendl matches. All of these guys, needless to say, were aggressive players.

Over time we've systematically gone through matches just because they were GS finals or other important matches, so that would offset, to some degree, any bias toward matches with high-winner counts. But I think it's likely that in our database, "aggressive" style matches still outnumber the ones with "conservative" styles.

Click to expand...

So from what you are saying it looks like something like this:

419
48% = 201 where winner did both things
52% = 218 where winner did only one

323 – 201 = 122 where winner had only more forced plays
293 – 201 = 92 where winner had only fewer UEs

(adds up to 214 instead of 218, I suppose due to rounding along the way)

So, in matches where the winner did only one of those two things, the break up is 57%-43% in favor of the player with more forcing plays.

If you suspect there may be a slight bias toward aggressive style in the selection of the whole set of 419 matches, this could suggest that on a large randomly selected sample it may turn out to be closer to 50-50. It could, but I am not sure this should necessarily be the case.

In the sample of 7 matches I examined, the winner did both things in only 1 of them. Another match had equal percentage of UEs on both sides. Of the remaining 5 matches, where the winner did only one of those two things, 3 of them were won by the more aggressive player, 2 were won by the player with fewer UEs. That's a 60%-40% break up, similar to your percentages.

Well actually I sorted my data tonight and it turns out most of my matches were won by the more aggressive player, ie, the one who made the greater number of forcing plays (winners + shots that force errors). That is the same thing you found. However, I also found out that most of my matches were won by the player who made fewer unforced errors.

The reason that's possible is that it's very common for both things to occur: the winner will make fewer unforced errors AND he will make the greater number of forcing plays.

Click to expand...

I think Jack Kramer would have smiled with self-satisfaction reading this.